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L 0-Norm and Total Variation for Wavelet Inpainting

  • Conference paper
Scale Space and Variational Methods in Computer Vision (SSVM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5567))

Abstract

In this paper, we suggest an algorithm to recover an image whose wavelet coefficients are partially lost. We propose a wavelet inpainting model by using L 0-norm and the total variation (TV) minimization. Traditionally, L 0-norm is replaced by L 1-norm or L 2-norm due to numerical difficulties. We use an alternating minimization technique to overcome these difficulties. In order to improve the numerical efficiency, we also apply a graph cut algorithm to solve the subproblem related to TV minimization. Numerical results will be given to demonstrate our advantages of the proposed algorithm.

The research is supported by MOE (Ministry of Education) Tier II project T207N2202 and IDM project NRF2007IDMIDM002-010. In addition, the support from SUG 20/07 is also gratefully acknowledged.

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Author information

Authors and Affiliations

  1. Division of Mathematical Science, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore

    Andy C. Yau & Xue-Cheng Tai

  2. Mathematics Institute, University of Bergen, Norway

    Xue-Cheng Tai

  3. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, Hong Kong

    Michael K. Ng

Authors
  1. Andy C. Yau
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  2. Xue-Cheng Tai
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  3. Michael K. Ng
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008, Bergen, Norway

    Xue-Cheng Tai

  2. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Oslo, Norway

    Knut Mørken

  3. Simula Research Laboratory, M. Linges v 17, Fornebu, P.O.Box 134, N-1325, Lysaker, Norway

    Marius Lysaker

  4. SINTEF ICT, Oslo, Norway

    Knut-Andreas Lie

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© 2009 Springer-Verlag Berlin Heidelberg

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Yau, A.C., Tai, XC., Ng, M.K. (2009). L 0-Norm and Total Variation for Wavelet Inpainting. In: Tai, XC., Mørken, K., Lysaker, M., Lie, KA. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2009. Lecture Notes in Computer Science, vol 5567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02256-2_45

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  • DOI: https://doi.org/10.1007/978-3-642-02256-2_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02255-5

  • Online ISBN: 978-3-642-02256-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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